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Title: U(3) and Pseudo-U(3) Symmetry of the Relativistic Harmonic Oscillator

Abstract

We show that a Dirac Hamiltonian with equal scalar and vector harmonic oscillator potentials has not only a spin symmetry but a U(3) symmetry and that a Dirac Hamiltonian with scalar and vector harmonic oscillator potentials equal in magnitude but opposite in sign has not only a pseudospin symmetry but a pseudo-U(3) symmetry. We derive the generators of the symmetry for each case.

Authors:
 [1]
  1. MS B283, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
Publication Date:
OSTI Identifier:
20699699
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review Letters; Journal Volume: 95; Journal Issue: 25; Other Information: DOI: 10.1103/PhysRevLett.95.252501; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; HAMILTONIANS; HARMONIC OSCILLATORS; POTENTIALS; RELATIVISTIC RANGE; SCALARS; SPIN; SYMMETRY; U-3 GROUPS; VECTORS

Citation Formats

Ginocchio, Joseph N. U(3) and Pseudo-U(3) Symmetry of the Relativistic Harmonic Oscillator. United States: N. p., 2005. Web. doi:10.1103/PhysRevLett.95.252501.
Ginocchio, Joseph N. U(3) and Pseudo-U(3) Symmetry of the Relativistic Harmonic Oscillator. United States. doi:10.1103/PhysRevLett.95.252501.
Ginocchio, Joseph N. Fri . "U(3) and Pseudo-U(3) Symmetry of the Relativistic Harmonic Oscillator". United States. doi:10.1103/PhysRevLett.95.252501.
@article{osti_20699699,
title = {U(3) and Pseudo-U(3) Symmetry of the Relativistic Harmonic Oscillator},
author = {Ginocchio, Joseph N.},
abstractNote = {We show that a Dirac Hamiltonian with equal scalar and vector harmonic oscillator potentials has not only a spin symmetry but a U(3) symmetry and that a Dirac Hamiltonian with scalar and vector harmonic oscillator potentials equal in magnitude but opposite in sign has not only a pseudospin symmetry but a pseudo-U(3) symmetry. We derive the generators of the symmetry for each case.},
doi = {10.1103/PhysRevLett.95.252501},
journal = {Physical Review Letters},
number = 25,
volume = 95,
place = {United States},
year = {Fri Dec 16 00:00:00 EST 2005},
month = {Fri Dec 16 00:00:00 EST 2005}
}